Doubly ionized helium ions are projected with a speed of 10 km s^...

The mass of a doubly ionized helium ion (alpha particle) is $m = 4 \times 1.66 \times 10^{-27} \text{ kg} = 6.64 \times 10^{-27} \text{ kg}$.

The charge of the ion is $q = 2e = 2 \times 1.6 \times 10^{-19} \text{ C} = 3.2 \times 10^{-19} \text{ C}$.

The velocity of the ion is $v = 10 \text{ km s}^{-1} = 10^4 \text{ m s}^{-1}$ and the uniform magnetic field is $B = 1.0 \text{ T}$.

The radius of the circular path is given by $r = \dfrac{mv}{qB}$.

Substituting the values:

$r = \dfrac{6.64 \times 10^{-27} \times 10^4}{3.2 \times 10^{-19} \times 1.0}$

$r = \dfrac{6.64}{3.2} \times 10^{-4} \text{ m}$

$r \approx 2.075 \times 10^{-4} \text{ m} \approx 2.1 \times 10^{-4} \text{ m}$